1 Polarised Two-Photon Absorption and Heterogeneous Fluorescence

Subscriber access provided by IDAHO STATE UNIV

Article

Polarised Two-Photon Absorption and Heterogeneous Fluorescence Dynamics in NAD(P)H Thomas S. Blacker, Nick Nicolaou, Michael R. Duchen, and Angus J Bain J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.9b01236 • Publication Date (Web): 25 Apr 2019 Downloaded from http://pubs.acs.org on April 26, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Polarised Two-Photon Absorption and Heterogeneous Fluorescence Dynamics in NAD(P)H Thomas S. Blacker1,2,3, Nick Nicolaou1, Michael R. Duchen3, Angus J. Bain1,2,*

1Department

of Physics & Astronomy, University College London, Gower Street, London WC1E

6BT, United Kingdom 2Centre

for Mathematics and Physics in the Life Sciences and Experimental Biology (CoMPLEX),

University College London, Gower Street, London WC1E 6BT, United Kingdom 3Research

Department of Cell & Developmental Biology, University College London, Gower Street,

London WC1E 6BT, United Kingdom

*Corresponding

author: [email protected]

1 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 51

Abstract Two-photon absorption (2PA) finds widespread application in biological systems, which frequently exhibit heterogeneous fluorescence decay dynamics corresponding to multiple species or environments. By combining polarised 2PA with time-resolved fluorescence intensity and anisotropy decay measurements, we show how the two-photon transition tensors for the components of a heterogeneous population can be separately determined, allowing structural differences between the two fluorescent states of the redox cofactor NAD(P)H to be identified. The results support the view that the two states correspond to alternate configurations of the nicotinamide ring, rather than folded and extended conformations of the entire molecule.


Page 3 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Introduction NAD and NADP are the principle biological cofactors involved in cellular redox metabolism1. The two molecules differ only by the presence of a phosphate group at the redox-inactive adenine end of NADP which is absent in NAD, as shown in Figure 1. This allows enzyme binding sites to be specific to either cofactor, enabling them to regulate contrasting biochemical pathways. The hydridecarrying nicotinamide ring is identical in the two molecules, and is responsible for the spectrally identical intrinsic fluorescence of their reduced forms, NADH and NADPH2. As alterations in the redox balance of the NAD and NADP pools are linked to a range of pathological conditions, NAD(P)H autofluorescence is often employed to investigate the role of metabolism in disease3. Fluorescence lifetime imaging microscopy (FLIM) is frequently used for this purpose; inside cells, the rate of decay of NAD(P)H fluorescence is dependent upon the enzymes to which the molecules are bound, allowing changes in the metabolic pathways activated in the diseased state to be detected in a label-free manner3–8. Maximising the information content of these measurements requires an increased understanding of how the photophysical quantities reported reflect the biochemical status of the target molecules.

Figure 1: Fluorescence in NADH and NADPH is localized to the nicotinamide moiety (a), where the amide group can adopt a cis (shown) or trans form by rotating 180° around the bond linking it to the pyridine ring. NADPH differs in structure from NADH by the presence of a phosphate group (b) at the adenine (c) end of the molecule.



Page 4 of 51

Even outside the highly crowded and non-uniform environment of the cell9, pure aqueous solutions of NADH or NADPH exhibit fluorescence decay dynamics indicative of an intrinsically heterogeneous population10–12. Two species are present in solutions of either molecule, a majority component (~90%) with a lifetime of approximately 0.4 ns and a minority component (~10%) of 0.8 ns10. However, the molecular origin of these species remains elusive. NAD(P)H is known to exist in two distinct configurations in solution, either folded with stacked adenine and nicotinamide rings or open and extended13, and parallels have perhaps naively been drawn between these two configurations and the two-component fluorescence decay of the molecule. For example, it has been suggested that the short lifetime state results from the folded configuration inducing dynamic quenching of the excited nicotinamide by the adenine moiety14,15. In contrast, the apparent nonexistence of the longer lifetime state in NAD(P)H analogues where the adenine moiety is absent led to suggestions that the nicotinamide and adenine rings form an exciplex with an enhanced quantum yield when stacked11,16. Recent ultrafast transient absorption studies appear to rule this out17. Additionally, inconsistencies between the decay amplitudes of the two components and the fraction of folded species measured by energy transfer13, alongside demonstrations of heterogeneous decay kinetics in nicotinamide mononucleotide12,18,19, suggest that the two fluorescence decay times arise from photophysical processes independent of the adenine moiety. In previous work, we demonstrated that the high rate of non-radiative excited state decay in NAD(P)H is due to small scale motion of the nicotinamide ring10. Power law models implied that the specific molecular motion associated with the conformational relaxation was identical in the two species, while an activated barrier crossing analysis suggested that the contrasting lifetimes of the two species arise from differences in the shape of the intramolecular potential energy surface experienced by the molecule while undergoing the motion. In the present study, we gain further insight into the photophysical origins of the two excited state populations in NAD(P)H through a


Page 5 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


novel approach to determine the individual two-photon absorption (2PA) properties of a multiple component system. Polarisation dependence of two-photon absorption A fundamental property of single-photon absorption (1PA) in an isotropic medium is that the transition probability is independent of the polarisation of the incident light20. However, for 2PA, the transition does not involve a simple dipolar rearrangement of electronic charge density but depends on a sum of products of all the allowed single-photon electric dipole transition moments between the ground, virtual, and final states. In essence, the first photon can be thought of as selecting a nonstationary virtual state that can be caused to undergo transitions to the final state by a second photon with only certain polarisations21,22. The polarisation dependence of 2PA is most commonly expressed through the polarisation ratio  , defined as the ratio of the 2PA cross sections for circularly and linearly polarised excitation23,



circ  2P lin  2P

(1)

The orientation-dependent transition probability for the absorption of two identical photons with polarisation vectors eˆ can be expressed as24,25,

A2PA  eˆ  S  eˆ

2

(2)

where S is the second rank tensor describing the angular properties of the two-photon transition. Transforming from the laboratory to molecular frame of reference and performing the necessary orientational averaging is most conveniently achieved using a spherical tensor formalism22,24–27. With this approach and assuming a planar transition, valid for NAD(P)H2,  can be written as,





Page 6 of 51

S XX  SYY 2  3S XX  SYY 2  12S XY 2 2 2 2 4S XX  SYY   2S XX  SYY   8S XY 

(3)

Normalising with respect to S XX yields22,24–27,



1  S 2  31  S 2  12 D 2 2 2 41  S   21  S   8D 2

(4)

where S  S YY S XX and D  S XY S XX . Values of  range from 1/4 to 3/2 depending on the symmetry of the participating electronic and vibrational states23,26–38 and local solvation effects39. The fluorescence anisotropies immediately after excitation by linearly and circularly polarised 2PA, Rlin 0  and Rcirc 0  respectively, are also determined by the components of S according to25,







1  9 1  S 2 cos 2  M  sin 2  M  41  S D sin  M cos  M  Rlin 0   1   2 2 7 21  S   1  S   4 D 2 



 





(5)



2 2 1  1  S   3 1  S   4 D 2  6 cos 2  M  sin 2  M 1  S 2  4 D1  S sin  M cos  M  Rcirc 0     7 1  S 2  31  S 2  12 D 2  (6)

where  M is the angle made by the emission transition dipole with respect to the x -axis of the molecular frame. Adopting a coordinate system in which this is defined by the direction of the 1PA transition dipole moment,  M can be determined from the initial anisotropy following 1PA40,

R1P 0  

2  3 cos 2  M  1   5 2 

(7)

Thus, given experimental measurements of Rlin 0  , Rcirc 0  , R1P 0  and  , the corresponding twophoton tensor components S and D can be calculated by solving Equations 4 to 7. This approach has previously been applied to perylene26,27,36 and enhanced green fluorescent protein (EGFP)25. As

 is independent of emission dipole moment orientation, it has also been measured by time


Page 7 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


averaged (steady state) fluorescence intensities following linearly and circularly polarised 2PA. However, as will be seen, this approach is no longer possible in systems with strongly heterogeneous fluorescence dynamics such as NAD(P)H and it is necessary to combine both time-resolved and steady state fluorescence measurements to determine the individual  values and corresponding transition tensor structures of each species. Polarised two-photon excited fluorescence in heterogeneous systems The simplest heterogeneous system corresponds to a mixed population containing two species

i  1,2 with relative (ground state) abundances  i (with  1   2  1 ), radiative rates k irad and fluorescence lifetimes  i . The fluorescence decays following linearly and circularly polarised twophoton excitation are given by,





I circ t   Acirc  1 1circ k1rad exp t  1    2 2circ k 2rad exp t  2 





I lin t   Alin  1 1lin k1rad exp t  1    2 2lin k 2rad exp t  2 

(8) (9)

where  icirc and  ilin are the cross sections for circularly and linearly polarised 2PA. The parameters

Acirc and Alin account for differences in the amount of fluorescence collected in each decay measurement arising, for example, from variations in laser power and collection times. In steady state measurements, Acirc and Alin can be made equal by measuring time-averaged fluorescence count rates under constant illumination intensity. Under these conditions, using Equations 8 and 9 to equate the ratio of absorption strengths to the ratio of fluorescence intensities29 gives, 



I circ t  I lin t 

 I t dt circ



0 

 I t dt



 1 1circ1   2 2circ 2  1 1lin1   2 2lin 2

lin

0


(10)


Page 8 of 51

where the bar signifies that the single  measurement reflects an underlying mixed population and

i are the quantum yields of each species. Rearranging for the individual polarisation ratios we find,   2 2lin 2   2 2circ 2  1circ  1  lin  1  1  1 1lin1   1 1lin1 

(11)

  2circ  1 1lin1   1 1circ1     1    lin     lin  2lin 2 2 2  2 2 2 

(12)

2 

Therefore, in addition to  , determining 1 and  2 would require knowledge of the relative ground state abundances of each species, their polarisation dependent 2PA cross sections and their quantum yields. However, we now show that this can also be achieved by combining ensemble polarised 2PA measurements with the parameters describing the fluorescence decays of a heterogeneous population for each excitation condition. These will have the form of Equations 8 and 9 for a two-component system such as NAD(P)H, which can be written in terms of the peak fluorescence intensities I circ 0  and I lin 0  by,





I circ t   I circ 0   1circ exp t  1    2circ exp t  2 





I lin t   I lin 0   1lin exp t  1    2lin exp t  2 

(13) (14)

where  1   2  1 . Equating the pre-exponential factors with Equations 8 and 9 gives,



circ 1

Acirc  1 1circ k1rad  I circ 0 

(15)



circ 2

Acirc  2 2circ k 2rad  I circ 0 

(16)


Page 9 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60




lin 1

Alin  1 1lin k1rad  I lin 0 

(17)



lin 2

Alin  2 2lin k 2rad  I lin 0 

(18)

Least squares fits to the intensity decay data yield values for the lifetimes  i and amplitudes  i . The constituent 2PA polarisation ratios are then given by,

1 

 1circ I circ 0  1circ Alin  I lin 0   1lin Acirc  1lin

(19)

2 

 2circ I circ 0  2circ Alin  I lin 0   2lin Acirc  2lin

(20)

Integrating Equations 8, 9, 13 and 14 to obtain the total fluorescence emission yields, 

 I t dt  A   circ

circ

1

   2 2circ 2   I circ 0 1circ 1   2circ 2 

(21)

   2 2lin 2   I lin 0 1lin 1   2lin 2 

(22)

circ 1 1

0



 I t dt  A   lin

lin

1

lin 1 1

0

Dividing Equation 21 by Equation 22 then gives, 

 I t dt circ

0 

 I t dt



 



 

Acirc  1 1circ1   2 2circ 2 I circ 0   1circ 1   2circ 2  Alin  1 1lin1   2 2lin 2 I lin 0   1lin 1   2lin 2







(23)

lin

0

Substituting Equation 10 and rearranging we obtain, Alin I lin 0    1lin 1   2lin 2     Acirc I circ 0   1circ 1   2circ 2 


(24)


Page 10 of 51

Substituting for Alin Acirc in Equations 19 and 20 then gives,

1 

 1circ  1lin

  1lin 1   2lin 2   circ  circ      2 2   1 1

(25)

2 

 2circ  2lin

  1lin 1   2lin 2   circ  circ  1  1   2  2 

(26)

These expressions thus allow the  values of the sub-populations to be determined by combining the fluorescence decay parameters with the conventional steady state  measurement. Our use of this approach to determine the underlying transition tensor structures of the 2PA processes that give rise to the bi-exponential fluorescence decay of NAD(P)H constitutes the first application of this method.


Page 11 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Experimental Methods NAD(P)H solutions NADH (N8129, Sigma-Aldrich, Dorset, UK) and NADPH (N7505, Sigma-Aldrich, Dorset, UK) were made up fresh on the day of experiment as 1mM solutions in Milli-Q water containing 10mM HEPES (H3375, Sigma-Aldrich, Dorset, UK) adjusted to pH 7.2. Laser sources For experiments with incident wavelengths between 625 nm and 720 nm, excitation was provided by the output of an optical parametric amplifier (OPA 9400, Coherent, Cambridgeshire, UK) pumped by a regeneratively amplified Ti:Sapphire laser (Mira 900F & RegA 9000, Coherent, Cambridgeshire, UK) operating at 800 nm with a repetition rate of 250 kHz. For wavelengths between 700 nm and 780 nm, the 76 MHz output of a Ti:Sapphire laser (Mira 900F, Coherent, Cambridgeshire, UK) was pulse picked to a repetition rate of 3.8 MHz (PulseSelect, APE, Berlin, Germany) for compatibility with the detection electronics. 360 nm excitation was obtained by frequency doubling the pulsepicked Ti:Sapphire output when tuned to 720 nm using a β-barium borate (BBO) crystal. Fluorescence measurements Both time-dependent and time-averaged polarised fluorescence measurements were made using a modular time correlated single photon counting (TCSPC) system (Ortec, Berkshire, UK) described previously10. The incident illumination was passed through a Glan-Laser polariser (Melles-Griot, New York, USA) to ensure vertical polarisation and a 25mm focal length achromatic doublet lens (Melles-Griot, New York, USA) was used to focus the beam onto the sample, held in a 3mm path length, 50μl quartz cuvette (Hellma, Essex, UK). Fluorescence was collected in a 90° excitationdetection geometry using a 25cm focal length lens and focussed into a multichannel plate photomultiplier tube (MCP-PMT, R3809U, Hamamatsu Photonics, Hertfordshire, UK) with a



Page 12 of 51

~100ps instrument response, passing through a 600 nm short pass filter, to eliminate laser breakthrough, and an emission polariser. This was set to the appropriate magic angle for absolute fluorescence intensity measurements, recorded from the count rate display of the TCSPC system. For time-resolved fluorescence measurements, a stepper motor rotated the emission polariser every 10 seconds to alternately transmit light polarised parallel or perpendicular to the symmetry axis of the excitation polarisation (vertical for linear, horizontal for circular). The corresponding decays I || t  and I  t  , spread across 512 channels covering 27 ns, were stored separately in computer memory. Emission events were registered for approximately 60 minutes for each set of measurements, resulting in a total number of photons collected of the order of 105 to 106, well below the 1 in 100 threshold for avoiding pulse pile-up effects41. Two-photon action cross section measurements Following the approach of Xu and Webb42, two-photon excitation of a sample by a pulsed laser source of wavelength  results in a time-averaged total fluorescence intensity of, I t  

4  gp   nC 2P Pt    fw 

2

(27)

where the fluorophore is present at a concentration C in a medium of refractive index n . Pt  is the time-averaged on-sample power of the illumination pulses with repetition rate f and g p is a dimensionless quantity dependent on the temporal profile of the laser pulses of duration (FWHM) w .  quantifies the fraction of the total fluorescence emitted by the fluorophore that is collected, taking into account emission filtering and the spectral efficiency of the detector. The product of the two-photon cross section  2P and the quantum yield  is the effective cross section for two-photon excited fluorescence, often referred to as the two-photon action cross section. This is frequently quoted in the units of Goeppert-Mayer (GM) where 1 GM is 10-50 cm4 s photon-1. The two-photon 12 ACS Paragon Plus Environment

Page 13 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


action cross sections of NADH and NADPH solutions could therefore be obtained by comparing the fluorescence intensity emitted at each excitation wavelength with that of reference standards with well characterised 2PA spectra42; p-bis(O-methylstyryl)benzene (bis-MSB, 15090, Sigma-Aldrich, Dorset, UK) in cyclohexane (227048, Sigma-Aldrich, Dorset, UK) covering 625 nm to 740 nm, and rhodamine B (LC6100, Lamdba Physik, Goettingen, Germany) in methanol (154903, Sigma-Aldrich, Dorset, UK) covering 700 nm to 780 nm. The bis-MSB reference spectrum was obtained by combining the relative spectrum provided by Kennedy et al.43 with the absolute cross section of 69 GM at 585 nm reported by Fisher et al.44. For rhodamine B, two-photon action cross sections were obtained online from the Zipfel lab at Cornell University, USA45. By rearranging Equation 27, assuming all incident laser properties remained constant between the reference and NAD(P)H measurements, the two-photon action cross sections could be calculated from,

 2P NAD(P)H   2P ref

nC ref nC NAD(P)H

I NAD(P)H t  I ref t 

(28)

Solvent refractive indices n were obtained from the literature46,47. Concentrations C were determined using published extinction coefficients48–50 and a USB spectrometer (USB4000, OceanOptics, Florida, USA) coupled to a xenon white light source. Rhodamine B and bis-MSB solutions were of the order of 10-5 M and 10-4 M respectively. The parameter  was calculated as,



max

max

min

min

 E  F  G d  E  d

(29)

where E   is the emission spectrum of the fluorophore obtained from the literature51–53. F   is the transmission ratio through the 600 nm short-pass emission filter measured using the absorption spectrometer described above. G   is the detection efficiency of the MCP-PMT at emission



Page 14 of 51

wavelength  , provided by the manufacturer. Values of  NAD(P)H  0.0751(±0.0003),  bis-MSB  0.0511(±0.0003) and  RhB  0.0249(±0.0001) were determined. Action cross sections were obtained between 625 nm and 780 nm at 5 nm intervals. Values at wavelengths with multiple measurements (due to both reference samples being applicable, or in the overlap between laser sources) are reported as uncertainty-weighted averages. Polarised two-photon excitation The excitation polarisation was varied between linear and circular by introducing a zero-order tuneable quarter wave plate (Alphalas, Goettingen, Germany) prior to the focusing lens. Circular polarisation was confirmed by observing that the power transmitted through a linear analysing polariser remained constant throughout its 360° rotation. Measurements of the fluorescence intensity were taken for each polarisation in turn, with the emission polariser set to the corresponding magic angle (54.7° and 35.3° from the vertical for linear and circular polarisation respectively). Five I circ t 

I lin t  pairs were taken at each wavelength, with  reported as the mean of these five

ratios. Fluorescence intensity decays Fluorescence decay curves were constructed from the polarised decays I || t  and I  t  using,

I t   I || t   2 I  t 

(30)

Fluorescence lifetimes were extracted from the I t  datasets using weighted least-squares tail fitting in OriginPro 2015 (OriginLab, Massachusetts, USA). Goodness-of-fit was determined using the reduced chi-squared parameter,


Page 15 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


 R2 

1 n 1 I measured t k   I model t k 2  2 n  l k 1  k

(31)

where n is the total number of time bins, l is the number of freely-varying parameters in the model and I measured t k  and I model t k  are the values of the fluorescence decay dataset and model at the time after excitation corresponding to bin k . As I || t  and I  t  constitute separate Poisson processes

I || t  and

with standard deviations

I  t  respectively, the fit weighting function can be obtained

by propagation of uncertainty through Equation 30, giving, 1



2 k



1 I || t k   4 I  t k 

(32)

For each time-resolved intensity measurement, a monoexponential fluorescence decay was a poor fit for the data, resulting in  R2 values of 33(±9). Addition of a second component improved this to a satisfactory 1.55(±0.07), with a tri-exponential model improving this value no further. All intensity decays were thus well described by bi-exponential functions as in Equations 8, 9, 13 and 14. The fraction of the total fluorescence emitted by each species i is then given by,

fi 



 

i

exp t  i dt



1

exp t  1    2 exp t  2 dt



 i i

 1 1  1   1  2

(33)



Time-resolved fluorescence anisotropy Anisotropy decays Rt  were constructed from I || t  and I  t  according to,

Rt  

I || t   I  t 

I || t   2 I  t 


(34)


Page 16 of 51

Anisotropy decay fitting was carried out in OriginPro 2015 using the corresponding weighting function10,

1

 k2



I t   4I t Rt  ||

k



k

I t k 

2

k

2

 2I || t k   2 I  t k Rt k   I || t k   I  t k 

(35)

In a two-species system such as NAD(P)H, the observed fluorescence anisotropy is given by the time-dependent weighted average of the component anisotropies, known as the associated anisotropy54,

Rt  

 1 R1 0 exp t  1  exp t  1rot   1   1 R2 0 exp t  2  exp t  2rot   1 exp t  1   1   1  exp t  2 

(36)

where R1 0  and R2 0  are the initial anisotropies of the two sub-populations and  1rot and  2rot are their rotational correlation times10. However, in this work, the time-resolved fluorescence anisotropies of NADH and NADPH arising from both linear and circularly polarised 2PA were suitably fit by a mono-exponential decay,



rot Rlin/circ t   Rlin/circ 0  exp  t  lin/circ



(37)

with average  R2 values of 1.46(±0.07).  R2 improved no further by increasing the complexity of the fitting function, indicating equal initial anisotropies and rotational correlation times in the two subpopulations, to within experimental uncertainties. Transition tensor structure Equations 4 to 7 were solved by using a Monte Carlo method in MATLAB (MathWorks, Massachusetts, USA). The measured Rlin 0  , Rcirc 0  , R1P 0  and  i were input alongside their uncertainties, defining the mean values and standard deviations of normal distributions of each parameter. Parameter values were picked at random from these four distributions using the 16 ACS Paragon Plus Environment

Page 17 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


normrnd() function and the equations were solved for this set of parameters using fsolve(). This was repeated 10,000 times, with the means and standard deviations of the S and D distributions obtained taken as the solution and its associated uncertainty. 2D polar plots of the tensor structures were constructed by expressing S in 2D polar coordinates,

A   cos 2   2 D sin  cos   S sin 2 

(38)

Error bounds were added to the polar plots by numerical propagation of error through Equation 38 in MATLAB.



Page 18 of 51

Results Two-photon absorption spectra Wavelengths ranging from 700 nm to 780 nm have been used to interrogate NAD(P)H in living tissues15,55, but its 2PA spectrum has never been fully determined below the Ti:sapphire tuning limit18,56,57. Using an optical parametric amplifier (OPA) to bypass this threshold, we measured the two-photon action cross section spectra of NADH and NADPH to be identical, peaking at 690 nm with a value of 0.15(±0.01) GM (see Figure 2). Without explicit knowledge of the relative ground state abundances  i , it is not possible to determine the individual two-photon cross sections of the sub-populations of NADH and NADPH. The values of the action cross sections reported here therefore represent an ensemble average. While the peak transition energy in both molecules was similar to that of 1PA, maximized at 340nm58, the two-photon resonance was narrower (FWHM 0.45eV vs. 0.72eV), as previously predicted for molecules in the Cs point group59 to which nicotinamide belongs60. The parameter  remained constant across the range of excitation wavelengths measured and was identical in NADH and NADPH, with a mean value of 0.787(±0.002). This is consistent with recent  measurements on NADH which assumed a homogeneous population61 and emphasises the lack of influence over the excited state photophysics of the nicotinamide chromophore by the distant phosphate group that differentiates between the two cofactors. In both NADH and NADPH, single- and two-photon excitation resulted in similar lifetimes for the two fluorescence decay components, in accordance with Kasha’s rule62, with average values of 0.362(±0.001) ns and 0.750(±0.006) ns (see Figure 3 and Table 1). Importantly, while linearly polarised excitation with both single- and two-photon absorption caused 84(±2)% of the short lifetime species to be excited, circularly polarised 2PA resulted in a significantly smaller proportion of the short lifetime state, at 78(±1)%. The individual polarisation ratios  i were calculated using 18 ACS Paragon Plus Environment

Page 19 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Equations 25 and 26, giving values of 1 and  2 that lie below and above  respectively. Averaging across the absorption spectrum yielded 0.73(±0.02) and 1.08(±0.07) for NADH with 0.76(±0.04) and 1.07(±0.09) for NADPH. This indicated that the two-photon transitions leading to emission from the short and longer lived states in these molecules have fundamentally different transition tensor structures.

Figure 2: Two-photon action cross section spectra and absorption polarisation ratios of (a) NADH and (b) NADPH in aqueous HEPES buffer. No differences in the 2PA absorption characteristics of NADH and NADPH were evident, including in their relative susceptibility to circularly and linearly polarised excitation which remained invariant to excitation wavelength across the two-photon resonance, averaging 0.776(±0.002). The two-photon action cross sections peak at 690 nm at a value of 0.15 GM. This occurs at a similar energy to the 1PA spectrum50,58 (c&d).



Page 20 of 51

Figure 3: Representative fluorescence intensity decays of 1mM NADH in aqueous solution excited at 705nm using (a) linearly polarised 2PA, (b) circularly polarised 2PA and (c) 1PA at 360 nm excitation. Weighted residuals (W.R.) are the ratio of the difference between the model and the data and the expected standard deviation, calculated using Equation 32.


Page 21 of 51

Linear

NADH

/ nm

1

 1 / ns

Circular

 2 / ns

1

 1 / ns

 2 / ns

705

0.73(±0.06) 0.344(±0.009) 0.69(±0.02) 0.69(±0.05) 0.315(±0.007) 0.70(±0.01)

715

0.86(±0.06) 0.367(±0.009) 0.93(±0.08) 0.78(±0.09)

725

0.86(±0.02) 0.380(±0.004) 0.78(±0.01) 0.72(±0.03) 0.330(±0.005) 0.68(±0.01)

735

0.83(±0.02) 0.366(±0.004) 0.77(±0.01) 0.78(±0.03) 0.350(±0.005) 0.76(±0.01)

745

0.82(±0.02) 0.378(±0.004) 0.78(±0.01) 0.86(±0.03) 0.391(±0.004) 0.84(±0.02)

755

0.87(±0.03) 0.395(±0.005) 0.84(±0.03) 0.80(±0.03) 0.357(±0.006) 0.78(±0.02)

765

0.88(±0.02) 0.396(±0.004) 0.90(±0.03) 0.82(±0.03) 0.365(±0.005) 0.81(±0.02)

0.34(±0.02)

0.79(±0.06)

Mean 0.85(±0.01) 0.379(±0.002) 0.78(±0.01) 0.79(±0.01) 0.357(±0.002) 0.74(±0.01) 360

NADPH

705

0.83(±0.02) 0.382(±0.005) 0.72(±0.02) 0.8(±0.2)

0.41(±0.03)

0.9(±0.1)

-

-

-

0.7(±0.1)

0.27(±0.01)

0.73(±0.01)

715

0.79(±0.05) 0.349(±0.008) 0.72(±0.02) 0.76(±0.06) 0.321(±0.009) 0.72(±0.02)

725

0.80(±0.06)

735

0.81(±0.04) 0.354(±0.007) 0.78(±0.02) 0.68(±0.08) 0.285(±0.009) 0.72(±0.02)

745

0.83(±0.04) 0.373(±0.007) 0.77(±0.02) 0.79(±0.05) 0.327(±0.009) 0.73(±0.02)

755

0.86(±0.05)

0.40(±0.01)

0.84(±0.05) 0.80(±0.04) 0.348(±0.008) 0.79(±0.02)

765

0.81(±0.06)

0.37(±0.01)

0.83(±0.03) 0.75(±0.06) 0.319(±0.009) 0.78(±0.02)

0.36(±0.01)

0.73(±0.03)

0.7(±0.1)

0.29(±0.01)

0.68(±0.02)

Mean 0.82(±0.02) 0.366(±0.003) 0.77(±0.01) 0.76(±0.02) 0.315(±0.003) 0.73(±0.01)

Combined

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


360

0.85(±0.03) 0.378(±0.006) 0.77(±0.02)

-

2PA

0.84(±0.01) 0.374(±0.002) 0.78(±0.01) 0.78(±0.01) 0.346(±0.002) 0.73(±0.01)

1PA

0.84(±0.02) 0.380(±0.004) 0.74(±0.01)

-

-

-

-

-

Table 1: Biexponential fitting parameters of fluorescence intensity decays of NADH and NADPH in aqueous buffer, across the tuning spectrum of the Ti:Sapphire laser and with single-photon excitation at 360 nm for comparison.



Page 22 of 51

Polarisation dependent 2P excitation spectra For the heterogeneous populations encountered in NAD(P)H, the 2PA cross section measured here will be a weighted average of the individual cross sections of the two species. Under these conditions, the steady state fluorescence intensity at each excitation wavelength can be related to the constituent concentrations C1  C 1 and C 2  C 2 using Equation 27 according to,

I  t  

4  gp  2  n Pt  C  11 1   2 2 2    fw 

(39)

Assuming a common radiative decay rate k rad for both species10, I  t   K  1 1 1   2 2 2   I  t  1  I  t 

2

(40)

where,

K  k rad

4  gp  2  n Pt  C   fw 

(41)

From the fluorescence decay dynamics (Equations 17 and 18) we know that the normalised preexponential factors are given by,

 1  k 1 1

(42)

 2  k 2 2

(43)

where k is a constant of proportionality. Using Equation 33, we can write, I  t  1  I  t 

 1 1  1 1   2 2


(44)

Page 23 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


I  t 

2

 2 2  1 1   2 2

 I  t 

(45)

Then, in terms of circular and linear polarisations we have,

I  t  1  I  t 

lin

I  t 

lin

lin

lin 2

 I  t 

 1lin 1  1lin 1   2lin 2

(46)

 2lin 2  1lin 1   2lin 2

(47)

circ

I  t  1

 1 I  t 

lin

I  t 

circ

  2 I  t 

lin

2

 1lin 1  1lin 1   2lin 2

(48)

 2lin 2  1lin 1   2lin 2

(49)

These quantities are plotted in Figure 4, where it can be seen that, in both NADH and NADPH, the highest intensity emission is observed with linearly polarised excitation of the short lifetime species. In contrast, the longer lifetime state displays similar emission intensities with circular and linear polarised two-photon excitation. This again implies differences in the 2PA tensor structures of the two species; circular polarisation favours off-diagonal elements, requiring simultaneous action by the applied electric field along two orthogonal axes, whereas linear polarisation favours diagonal transition terms, corresponding to two parallel transition moments requiring simultaneous action twice along a single symmetry axis22.



Page 24 of 51

Figure 4: Relative fluorescence intensity of the two NAD(P)H species as a function of excitation wavelength, with the short lifetime linearly polarised peak of each molecule arbitrarily scaled to 1. While the short lifetime species favours linearly polarised excitation in both NADH and NADPH (a&b), the longer lifetime species exhibits similar fluorescence intensities with both excitation polarisations (c&d). Shaded areas represent uncertainty bounds.

Individual transition tensor structures The initial single-photon fluorescence anisotropies in NADH and NADPH were found to be 0.36(±0.07) and 0.35(±0.05) respectively, corresponding to transition dipole moment angles  M of 20(±10)° for NADH and 16(±9)° for NADPH (see Figure 5 and Table 2). Averaged across all excitation wavelengths, the initial anisotropies following linearly and circularly polarised two-photon absorption of NADH were 0.52(±0.02) and -0.24(±0.03). For NADPH, the corresponding values were 0.55(±0.05) and -0.25(±0.04). The circularly polarised rotational correlation times for NADH 24 ACS Paragon Plus Environment

Page 25 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


of 0.253(±0.002) ns and NADPH of 0.304(±0.005) ns were faster than the corresponding linearly polarised measurements of 0.323(±0.002) ns and 0.336(±0.003) ns. Differences between linear and circularly polarised fluorescence anisotropy decay times in a homogeneous population can be indicative of the presence of off diagonal transition tensor elements26,27. Treating NADH and NADPH as a homogeneous systems (using  ) and solving Equations 4 to 7 suggested a primarily single element tensor, as shown in Table 3. However, solving for the tensor elements with the separate values of 1 and  2 , differences in 2PA between the two species became apparent. Specifically, in both NADH and NADPH, while the short lifetime state was dominated by a single element, the longer lifetime state contained a significant negative diagonal element of S  -0.3(±0.1). Polar plots of the 2PA tensors63 of the two species are shown in Figure 6, which demonstrate that the effect of the significant negative value of S in the longer lifetime species is the addition of negative amplitude lobes to the polar plot and a rotation of the principle axis of the tensor. The angle of rotation is calculated by differentiating Equation 38 to find the turning point,

 A   2 D cos 2 turn  S  1sin 2 turn  0       turn

1 2

 2D   1 S 

 turn  arctan

The combined values in Table 3 imply  turn  3(±5)° for the long lifetime species.


(50)

(51)


Page 26 of 51

Figure 5: Representative fluorescence anisotropy decays of 1mM NADH in aqueous solution excited at 705nm using (a) linearly polarised 2PA, (b) circularly polarised 2PA and (c) 1PA at 360 nm excitation. Weighted residuals (W.R.) are the ratio of the difference between the model and the data and the expected standard deviation, calculated using Equation 35.


Page 27 of 51

NADPH

NADH

Linear

Combined

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Circular

 / nm

RL 0 

 Lrot / ns

RC 0 

 Crot / ns

705

0.53(±0.07)

0.277(±0.006)

-0.2(±0.1)

0.27(±0.01)

715

0.5(±0.1)

0.279(±0.005)

-0.28(±0.08)

0.260(±0.007)

725

0.55(±0.08)

0.290(±0.004)

-0.25(±0.08)

0.264(±0.008)

735

0.5(±0.1)

0.324(±0.009)

-0.25(±0.08)

0.244(±0.007)

745

0.50(±0.03)

0.346(±0.002)

-0.23(±0.05)

0.252(±0.004)

755

0.52(±0.08)

0.323(±0.005)

-0.24(±0.08)

0.246(±0.007)

765

0.5(±0.1)

0.360(±0.007)

-0.25(±0.08)

0.249(±0.007)

Mean

0.52(±0.02)

0.323(±0.002)

-0.24(±0.03)

0.253(±0.002)

360

0.36(±0.07)

0.258(±0.006)

-

-

705

0.5(±0.3)

0.28(±0.02)

-0.3(±0.1)

0.32(±0.01)

715

0.5(±0.1)

0.308(±0.008)

-0.2(±0.1)

0.28(±0.01)

725

0.5(±0.1)

0.364(±0.007)

-0.3(±0.1)

0.35(±0.02)

735

0.6(±0.1)

0.316(±0.008)

-0.3(±0.1)

0.29(±0.02)

745

0.6(±0.1)

0.357(±0.007)

-0.25(±0.08)

0.35(±0.01)

755

0.6(±0.1)

0.338(±0.009)

-0.2(±0.1)

0.30(±0.02)

765

0.5(±0.2)

0.364(±0.01)

-0.2(±0.2)

0.25(±0.01)

Mean

0.55(±0.05)

0.336(±0.003)

-0.25(±0.04)

0.304(±0.005)

360

0.35(±0.05)

0.42(±0.01)

-

-

2PA

0.52(±0.02)

-

-0.25(±0.02)

-

1PA

0.36(±0.04)

-

-

-

Table 2: Fluorescence anisotropy decay parameters of NADH and NADPH in aqueous buffer, across the tuning spectrum of the Ti:Sapphire laser and with single-photon excitation at 360 nm for comparison.



Short Lifetime Species

Long Lifetime Species

Page 28 of 51

Homogeneous Treatment

S

D

S

D

S

D

NADH

0(±0.2)

0(±0.3)

-0.3(±0.1)

0.1(±0.2)

-0.06(±0.04)

0(±0.2)

NADPH

0(±0.1)

0(±0.2)

-0.3(±0.1)

0.1(±0.2)

-0.06(±0.03)

0(±0.1)

Combined

-0.04(±0.03)

0(±0.2)

-0.31(±0.05)

0.1(±0.1)

-0.07(±0.03)

0(±0.1)

Table 3: Tensor components for the two fluorescence decay components of NADH and NADPH. In both molecules, the long lifetime species exhibits a significant negative diagonal element, in contrast to the primarily single element short lifetime species. These differences could not be observed if the analysis assumed a homogeneous system. As the tensor components of the two molecules are identical, suggesting that the phosphate group which differentiates between them plays no role in the transition, the datasets were combined to reduce uncertainties before plotting in Figure 6.


Page 29 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 6: 2PA tensor polar plots for the combined NADH and NADPH data displayed in Table 3. The distance of the line to the origin dictates the transition amplitude at each angle. Red and blue lines indicate positive and negative amplitudes, respectively. Shaded areas represent uncertainty bounds. While the short lifetime tensor is dominated by a single element (a), the long lifetime species exhibits negative lobes which rotate the direction of maximum absorption by around 3° from the single-photon S0-S1 transition (b). These features could not be resolved if the excited state population was treated as homogeneous (c).



Page 30 of 51

Discussion We have identified clear differences in the structures of the two-photon transitions giving rise to the short and long lifetime fluorescent species of NADH and NADPH. Our work therefore rules out two proposed, but unproven, mechanisms for the heterogeneous intensity decay dynamics observed. Dynamic quenching by the adenine moiety in the folded state has been widely assumed14,15, whilst a kinetic scheme involving a single emitting excited state species with conversion into a nonfluorescent product has also been proposed12. As these are both post-excitation phenomena, the 2PA transition would be common to both components, which is clearly not observed here. Opposing signs of S XX and S YY in the 2PA tensor of the long lifetime NAD(P)H species caused negative lobes that were absent in the short lifetime species. Parallels can be drawn between these results and the behaviour of the 1Lb absorption band of indole64,65. Callis63 observed negative lobes to be present in the 2PA tensor of pure indole, which were then reduced significantly upon the addition of a single methyl group to the pyrole ring. The difference in the 2PA tensors of the short and long lifetime species of NAD(P)H clearly cannot be attributed to differing substituent groups. However, alternate configurations of the nicotinamide ring have previously been suggested to play a role in the spectral properties of the molecule, particularly those involving the amide group2,13. Both 1PA and 2PA are predicted to be accompanied by charge transfer from the pyridine ring nitrogen to the oxygen of the amide group18, which favours the cis conformation displayed in Figure 166. A trans conformation, in which the amide group is rotated by 180°, can also be adopted67 (see Figure 1). The contrasting electronic rearrangement taking place following absorption in each species, due to the differing location of the oxygen atom relative to the ring nitrogen in the two configurations, may then be sufficient to alter the symmetry of the two-photon transition. Enzyme binding sites are known to favour the trans conformation of NAD(P)H67 in addition to altering its local electrostatic environment68. It is possible that these effects could also contribute to the photophysical alterations


Page 31 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


induced by the binding of NADH and NADPH to different enzymes. This will be the subject of future studies. Quantum chemical calculations have predicted a single element 2PA tensor for the nicotinamide chromophore as we observed in the short lifetime species, with the principle axis collinear to the 1PA transition dipole18. These calculations involved a free energy minimisation step, so were likely carried out on the cis configuration of the amide group as the free energy of the trans form is 1 kcal mol-1 higher67. For a difference in Gibbs free energy G , the relative amounts of each species present at equilibrium are given by69,

 cis 

1 exp G RT   1

(52)

1 expG RT   1

(53)

 trans 

where R is the universal gas constant and T is the temperature. At a lab temperature of 21°C, 85% of the NAD(P)H population would be expected to assume the cis configuration and 15% the trans configuration. These values are in precise agreement with the linearly polarised decay amplitudes we measure here. If the two components in the fluorescence decay of NAD(P)H do indeed correspond to the cis and trans form of the nicotinamide ring, this would imply  1lin   cis  0.85 and  2lin   trans  0.15. By Equations 42 and 43, the linearly polarised 2PA cross sections of the two species would therefore be equal, which could explain the absence of characteristic spectral features corresponding to each fluorescent species in the absorption spectra2,50,58. The circularly polarised 2PA cross section of the short lifetime species would then be a factor of 1  0.74 lower, causing the smaller contribution of this component to the fluorescence decay with circularly polarised two-photon excitation.



Page 32 of 51

Our previous work suggested the contrasting lifetimes of the two fluorescent species of NAD(P)H arise from differences in the shape of the potential energy surfaces encountered as they undergo nonradiative conformational relaxation back to the ground state10. Specifically, the frequency of the initial potential energy well of short lifetime species was double that of the long lifetime species, leading to a non-radiative rate twice as large. The small magnitudes of the initial well frequencies were consistent with small scale motion for the conformational relaxation, such as the puckering that occurs in the nicotinamide ring70. Interestingly, this puckering is known to be altered in the trans state67, which could lead to the differences in well frequencies and therefore the different lifetimes. Time-resolved fluorescence anisotropy measurements are potentially sensitive to such differences in molecular structure. In the present study, rapid mono-exponential anisotropy decay times (approaching the MCP-PMT response) were observed for NAD(P)H. In our previous work10, the increased fluorescence intensity afforded by 1PA, together with the enhanced quantum yield and slower (nanosecond) rotational diffusion times of NAD(P)H in more viscous environments, revealed associated (heterogeneous) anisotropy decay dynamics with distinct rotational diffusion times of the two sub-populations. In both NADH and NADPH, the rotational diffusion rates of the long lifetime species were on average 1.9 times lower than those of the short lifetime species. From the StokesEinstein-Debye equation, this implies differing form factors or hydrodynamic volumes for the two species10. The amide group lies approximately 20° out of the plane of the nicotinamide ring in the trans configuration67, which could provide a physical basis for these observations. It had previously been shown16 that the potential energy barrier encountered by both species during conformational relaxation was equal at 1.5 kcal mol-1. The barrier encountered during the cis-trans transition is almost five times larger67. Alongside our previous data suggesting that the variation in non-radiative decay rate with viscosity was inconsistent with the internal conversion involving an isomerisation10, this implies that no switching between the cis and trans configurations occurs in the excited state dynamics. The heterogeneous fluorescence decay dynamics of NAD(P)H solutions 32 ACS Paragon Plus Environment

Page 33 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


therefore correspond to two distinct ground state species, with separate 2PA transition tensors and dissimilar lifetimes due to different conformational relaxation rates.



Page 34 of 51

Conclusions Knowledge of the 2PA polarisation ratio  has proven to be an invaluable means of determining the 2PA transition tensor and the symmetry of the participating states. Measurement of  has, until now, been the preserve of steady state or time-averaged fluorescence intensity measurements. While this is a valid approach in the study of 2PA in homogeneous populations, we have shown that for heterogeneous systems  is related to the constituent 2PA transitions by a ratio of decay amplitudes and lifetimes which steady state measurements cannot provide. The introduction of time-resolved fluorescence measurements is therefore required to extract the individual  values of each species. It is then possible to determine the 2D tensor elements of the individual 2PA transitions by introducing linear and circularly polarised fluorescence anisotropy measurements. We have utilised this approach to show, for the first time, that the bi–exponential fluorescence decay in NAD(P)H arises from two distinct 2PA processes with different transition tensor structures. Our results point to the existence of structural differences in the nicotinamide ring of the two sub-populations as the underlying cause of the observed difference in their non-radiative activated barrier crossing decay rates10, and do not accord with post-absorption mechanisms such as intermolecular quenching or excited state reactions12,14,15. An enhanced understanding of NAD(P)H photophysics will assist in promoting its use as an accurate, endogenously fluorescent reporter of intercellular biochemistry3–8. The approaches outlined here will also find immediate application in other biological fluorescence studies where heterogeneous populations are known to exist, in particular those involving fluorescent proteins71,72 and the state restriction observed in their Förster resonance energy transfer (FRET) dynamics25,54,73.


Page 35 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Acknowledgements This work was funded by BBSRC grant BB/P018726/1, "New approaches to studying redox metabolism using time-resolved NAD(P)H fluorescence and anisotropy".



Page 36 of 51

References (1)

Ying, W. NAD+/NADH and NADP+/NADPH in Cellular Functions and Cell Death: Regulation and Biological Consequences. Antioxid Redox Signal 2008, 10 (2), 179–206.

(2)

De Ruyck, J. J.; Famerée, M.; Wouters, J.; Perpète, E. A.; Preat, J.; Jacquemin, D. Towards the Understanding of the Absorption Spectra of NAD(P)H/NAD(P)+ as a Common Indicator of Dehydrogenase Enzymatic Activity. Chem. Phys. Lett. 2007, 450 (1-3), 119–122.

(3)

Blacker, T. S.; Duchen, M. R. Investigating Mitochondrial Redox State Using NADH and NADPH Autofluorescence. Free Radic. Biol. Med. 2016, 100, 53–65.

(4)

Horilova, J.; Mateasik, A.; Revilla-i-Domingo, R.; Raible, F.; Chorvat Jr, D.; Chorvatova, A. M. Fingerprinting of Metabolic States by NAD (P) H Fluorescence Lifetime Spectroscopy in Living Cells: A Review. Med. Photonics 2015, 27, 62–69.

(5)

Schaefer, P. M.; Kalinina, S.; Rueck, A.; von Arnim, C. A. F.; von Einem, B. NADH Autofluorescence—A Marker on Its Way to Boost Bioenergetic Research. Cytom. Part A 2018.

(6)

Kolenc, O. I.; Quinn, K. P. Evaluating Cell Metabolism Through Autofluorescence Imaging of NAD (P) H and FAD. Antioxid. Redox Signal. 2018.

(7)

Blacker, T. S.; Sewell, M. D. E.; Szabadkai, G.; Duchen, M. R. Metabolic Profiling of Live Cancer Tissues Using NAD (P) H Fluorescence Lifetime Imaging. In Cancer Metabolism; Springer, 2019; pp 365–387.

(8)

Blacker, T. S.; Duchen, M. R. Characterizing Metabolic States Using Fluorescence Lifetime Imaging Microscopy (FLIM) of NAD(P)H. In Neuromethods; 2017; Vol. 123.

(9)

Lee, H. B.; Cong, A.; Leopold, H.; Currie, M.; Boersma, A.; Sheets, E. D.; Heikal, A. A. Rotational and Translational Diffusion of Size-Dependent Fluorescent Probes in


Page 37 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Homogeneous and Heterogeneous Environments. Phys. Chem. Chem. Phys. 2018. (10)

Blacker, T. S.; Marsh, R. J.; Duchen, M. R.; Bain, A. J. Activated Barrier Crossing Dynamics in the Non-Radiative Decay of NADH and NADPH. Chem. Phys. 2013, 422, 184–194.

(11)

Visser, A. J. W. G.; Hoek, A. van. The Fluorescence Decay of Reduced Nicotinamides in Aqueous Solution after Excitation with a UV-Mode Locked Locked Ar ION Laser. Photochem. Photobiol. 1981, 33 (1), 35–40.

(12)

Gafni, A.; Brand, L. Fluorescence Decay Studies of Reduced Nicotinamide Adenine Dinucleotide in Solution and Bound to Liver Alcohol Dehydrogenase. Biochemistry 1976, 15 (15), 3165–3171.

(13)

Hull, R. V.; Conger 3rd, P. S.; Hoobler, R. J.; Conger, P. S.; Hoobler, R. J. Conformation of NADH Studied by Fluorescence Excitation Transfer Spectroscopy. Biophys Chem 2001, 90 (1), 9–16.

(14)

Ghukasyan, V. V; Kao, F.-J. Monitoring Cellular Metabolism with Fluorescence Lifetime of Reduced Nicotinamide Adenine Dinucleotide. J. Phys. Chem. C 2009, 113 (27), 11532– 11540.

(15)

Skala, M. C.; Riching, K. M.; Bird, D. K.; Gendron-Fitzpatrick, A.; Eickhoff, J.; Eliceiri, K. W.; Keely, P. J.; Ramanujam, N. In Vivo Multiphoton Fluorescence Lifetime Imaging of Protein-Bound and Free Nicotinamide Adenine Dinucleotide in Normal and Precancerous Epithelia. J. Biomed. Opt. 2007, 12 (2), 24014.

(16)

Couprie, M. E.; Mérola, F.; Tauc, P.; Garzella, D.; Delboulbé, A.; Hara, T.; Billardon, M. First Use of the UV Super-ACO Free-Electron Laser: Fluorescence Decays and Rotational Dynamics of the NADH Coenzyme. Rev. Sci. Instrum. 1994, 65 (5), 1485.

(17)

Heiner, Z.; Roland, T.; Leonard, J.; Haacke, S.; Groma, G. I. Kinetics of Light-Induced Intramolecular Energy Transfer in Different Conformational States of NADH. J. Phys. Chem. 37 ACS Paragon Plus Environment


Page 38 of 51

B 2017, 121 (34), 8037–8045. (18)

Kierdaszuk, B.; Malak, H.; Gryczynski, I.; Callis, P.; Lakowicz, J. R. Fluorescence of Reduced Nicotinamides Using One- and Two-Photon Excitation. Biophys. Chem. 1996, 62 (13), 1–13.

(19)

Krishnamoorthy, G.; Periasamy, N.; Venkataraman, B. On the Origin of Heterogeneity of Fluorescence Decay Kinetics of Reduced Nicotinamide Adenine Dinucleotide. Biochem Biophys Res Commun 1987, 144 (1), 387–392.

(20)

Brink, D. M.; Satchler, G. R. Angular Momentum; Clarendon Press, 1968.

(21)

Bray, R. G.; Hochstrasser, R.-M. Two-Photon Absorption by Rotating Diatomic Molecules. Mol. Phys. 1976, 31 (4), 1199–1211.

(22)

Bain, A. J. Multiphoton Processes. In Photonics; 2015; Vol. 1, pp 279–320.

(23)

Drucker, R. P.; McClain, W. M. Polarized Two-Photon Studies of Biphenyl and Several Derivatives. J. Chem. Phys. 1974, 61 (7), 2609–2615.

(24)

Wan, C.; Johnson, C. K. Time-Resolved Two-Photon Induced Anisotropy Decay: The Rotational Diffusion Regime. J. Chem. Phys. 1994, 101 (12), 10283.

(25)

Masters, T. A.; Marsh, R. J.; Blacker, T. S.; Armoogum, D. A.; Larijani, B.; Bain, A. J. Polarized Two-Photon Photoselection in EGFP: Theory and Experiment. J. Chem. Phys. 2018, 148, 134311.

(26)

Ryderfors, L.; Mukhtar, E.; Johansson, L. B.-A. The Symmetry of Two-Photon Excited States as Determined by Time-Resolved Fluorescence Depolarization Experiments. J. Phys. Chem. A 2007, 111 (45), 11531–11539.

(27)

Ryderfors, L.; Mukhtar, E.; Johansson, L. B.-Å. Excited-State Symmetry and Reorientation Dynamics of Perylenes in Liquid Solutions: Time-Resolved Fluorescence Depolarization 38 ACS Paragon Plus Environment

Page 39 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Studies Using One-and Two-Photon Excitation. J. Phys. Chem. A 2008, 112 (26), 5794–5803. (28)

Callis, P. R. Two-Photon-Induced Fluorescence. Annu Rev Phys Chem 1997, 48, 271–297.

(29)

Callis, P. R.; Scott, T. W.; Albrecht, A. C. Polarized Two-Photon Fluorescence Excitation Studies of Pyrimidine. J. Chem. Phys. 1981, 75 (12), 5640–5646.

(30)

Berg, J. O.; Parker, D. H.; El-Sayed, M. A. Symmetry Assignment of Two-Photon States from Polarization Characteristics of Multiphoton Ionization Spectra. J. Chem. Phys. 1978, 68 (12), 5661–5663.

(31)

Scott, T. W.; Albrecht, A. C. A Rydberg Transition in Benzene in the Condensed Phase: TwoPhoton Fluorescence Excitation Studies. J. Chem. Phys. 1981, 74 (7), 3807–3812.

(32)

Scott, T. W.; Haber, K. S.; Albrecht, A. C. Two-Photon Photoselection in Rigid Solutions: A Study of the B 2 U← A 1 G Transition in Benzene. J. Chem. Phys. 1983, 78 (1), 150–157.

(33)

Monson, P. R.; McClain, W. M. Complete Polarization Study of the Two-Photon Absorption of Liquid 1-Chloronaphthalene. J. Chem. Phys. 1972, 56 (10), 4817–4825.

(34)

Yu, J.-A.; Nocera, D. G.; Leroi, G. E. Two-Photon Excitation Spectrum of Perylene in Solution. Chem. Phys. Lett. 1990, 167 (1-2), 85–89.

(35)

Faidas, H.; Siomos, K. Two-Photon Excitation Spectroscopy of Benzene and Toluene in Nonpolar Liquids. J. Mol. Spectrosc. 1988, 130 (2), 288–302.

(36)

Pauls, S. W.; Hedstrom, J. F.; Johnson, C. K. Rotational Relaxation of Perylene in N-Alcohols and N-Alkanes Studied by Two-Photon-Induced Anisotropy Decay. Chem. Phys. 1998, 237 (1), 205–222.

(37)

Dick, B.; Gonska, H.; Hohlneicher, G. Two Photon Spectroscopy of Dipole Forbidden Transitions III. Experimental Determination of Two Photon Absorption Spectra Including Polarization Control. Berichte der Bunsengesellschaft für Phys. Chemie 1981, 85 (8), 746– 39 ACS Paragon Plus Environment


Page 40 of 51

754. (38)

Vivas, M. G.; Diaz, C.; Echevarria, L.; Mendonca, C. R.; Hernández, F. E.; De Boni, L. TwoPhoton Circular–Linear Dichroism of Perylene in Solution: A Theoretical–Experimental Study. J. Phys. Chem. B 2013, 117 (9), 2742–2747.

(39)

Wirth, M. J.; Koskelo, A. C.; Mohler, C. E. Study of Solvation Symmetry by Two-Photon Polarization Measurements. J. Phys. Chem. 1983, 87 (22), 4395–4400.

(40)

Chuang, T. J.; Eisenthal, K. B. Theory of Fluorescence Depolarization by Anisotropic Rotational Diffusion. J. Chem. Phys. 1972, 57 (12), 5094–5097.

(41)

Salthammer, T. Numerical Simulation of Pile-up Distorted Time-Correlated Single Photon Counting (TCSPC) Data. J. Fluoresc. 1992, 2 (1), 23–27.

(42)

Xu, C.; Webb, W. W. Measurement of Two-Photon Excitation Cross Sections of Molecular Fluorophores with Data from 690 to 1050 Nm. J. Opt. Soc. Am. B 1996, 13 (3), 481–491.

(43)

Kennedy, S. M.; Lytle, F. E. P-Bis (O-Methylstyryl) Benzene as a Power-Squared Sensor for Two-Photon Absorption Measurements between 537 and 694 Nm. Anal. Chem. 1986, 58 (13), 2643–2647.

(44)

Fisher, W. G.; Wachter, E. A.; Lytle, F. E.; Armas, M.; Seaton, C. Source-Corrected TwoPhoton Excited Fluorescence Measurements between 700 and 880 Nm. Appl. Spectrosc. 1998, 52 (4), 536–545.

(45)

Zipfel, W. R. https://zipfellab.bme.cornell.edu/cross_sections.html.

(46)

Schiebener, P.; Straub, J.; Levelt Sengers, J. M. H.; Gallagher, J. S. Refractive Index of Water and Steam as Function of Wavelength, Temperature and Density. J. Phys. Chem. Ref. data 1990, 19 (3), 677–717.

(47)

Rheims, J.; Köser, J.; Wriedt, T. Refractive-Index Measurements in the near-IR Using an 40 ACS Paragon Plus Environment

Page 41 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Abbe Refractometer. Meas. Sci. Technol. 1997, 8 (6), 601. (48)

Xue-Feng, D.; Liang-Jian, W.; Xiang, Z.; Ya-Yun, D.; Xing-Chen, Y.; Li, Z.; Meng-Chao, L.; Hao, C.; Jun, C. Measurement of the Fluorescence Quantum Yield of Bis-MSB. Chinese Phys. C 2015, 39 (12), 126001.

(49)

Faraggi, M.; Peretz, P.; Rosenthal, I.; Weinraub, D. Solution Properties of Dye Lasers. Rhodamine B in Alcohols. Chem. Phys. Lett. 1984, 103, 310–314.

(50)

Ziegenhorn, J.; Senn, M.; Bücher, T. Molar Absorptivities of Beta-NADH and Beta-NADPH. Clin. Chem. 1976, 22 (2), 151–160.

(51)

Du, H.; Fuh, R. C. A.; Li, J.; Corkan, L. A.; Lindsey, J. S. PhotochemCAD: A ComputerAided Design and Research Tool in Photochemistry. Photochem. Photobiol. 1998, 68 (2), 141–142.

(52)

Patterson, G. H.; Knobel, S. M.; Arkhammar, P.; Thastrup, O.; Piston, D. W. Separation of the Glucose-Stimulated Cytoplasmic and Mitochondrial NAD(P)H Responses in Pancreatic Islet Beta Cells. Proc Natl Acad Sci U S A 2000, 97 (10), 5203–5207.

(53)

Lakowicz, J. R.; Gryczynski, I. Characterization of P-Bis (O-Methylstyryl) Benzene as a Lifetime and Anisotropy Decay Standard for Two-Photon Induced Fluorescence. Biophys. Chem. 1993, 47 (1), 1–7.

(54)

Blacker, T. S.; Chen, W.; Avezov, E.; Marsh, R. J.; Duchen, M. R.; Kaminski, C. F.; Bain, A. J. Investigating State Restriction in Fluorescent Protein FRET Using Time-Resolved Fluorescence and Anisotropy. J. Phys. Chem. C 2017, 121 (3), 1507–1514.

(55)

Blacker, T. S.; Mann, Z. F.; Gale, J. E.; Ziegler, M.; Bain, A. J.; Szabadkai, G.; Duchen, M. R. Separating NADH and NADPH Fluorescence in Live Cells and Tissues Using FLIM. Nat. Commun. 2014, 5, 3936.



(56)

Page 42 of 51

Zipfel, W. R.; Williams, R. M.; Christie, R.; Nikitin, A. Y.; Hyman, B. T.; Webb, W. W. Live Tissue Intrinsic Emission Microscopy Using Multiphoton-Excited Native Fluorescence and Second Harmonic Generation. Proc. Natl. Acad. Sci. U. S. A. 2003, 100 (12), 7075–7080.

(57)

Huang, S.; Heikal, A. A.; Webb, W. W. Two-Photon Fluorescence Spectroscopy and Microscopy of NAD(P)H and Flavoprotein. Biophys J 2002, 82 (5), 2811–2825.

(58)

Rover Jr, L.; Fernandes, J. C. B.; de Oliveira Neto, G.; Kubota, L. T.; Katekawa, E.; Serrano, S. H. P. Study of NADH Stability Using Ultraviolet–visible Spectrophotometric Analysis and Factorial Design. Anal. Biochem. 1998, 260 (1), 50–55.

(59)

de Wergifosse, M.; Elles, C. G.; Krylov, A. I. Two-Photon Absorption Spectroscopy of Stilbene and Phenanthrene: Excited-State Analysis and Comparison with Ethylene and Toluene. J. Chem. Phys. 2017, 146 (17), 174102.

(60)

Ramalingam, S.; Periandy, S.; Govindarajan, M.; Mohan, S. FT-IR and FT-Raman Vibrational Spectra and Molecular Structure Investigation of Nicotinamide: A Combined Experimental and Theoretical Study. Spectrochim. Acta Part A Mol. Biomol. Spectrosc. 2010, 75 (5), 1552– 1558.

(61)

Vasyutinskii, O. S.; Smolin, A. G.; Oswald, C.; Gericke, K. H. Polarized Fluorescence in NADH under Two-Photon Excitation with Femtosecond Laser Pulses. Opt. Spectrosc. 2017, 122 (4), 602–606.

(62)

Kasha, M. Characterization of Electronic Transitions in Complex Molecules. Discuss. Faraday Soc. 1950, 9, 14.

(63)

Callis, P. R. On the Theory of Two-Photon Induced Fluorescence Anisotropy with Application to Indoles. J. Chem. Phys. 1993, 99 (1), 27–37.

(64)

Albinsson, B.; Norden, B. Excited-State Properties of the Indole Chromophore: Electronic Transition Moment Directions from Linear Dichroism Measurements: Effect of Methyl and 42 ACS Paragon Plus Environment

Page 43 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Methoxy Substituents. J. Phys. Chem. 1992, 96 (15), 6204–6212. (65)

Sobolewski, A. L.; Domcke, W. Ab Initio Investigations on the Photophysics of Indole. Chem. Phys. Lett. 1999, 315, 293–298.

(66)

Kumar, M.; Jaiswal, S.; Singh, R.; Srivastav, G.; Singh, P.; Yadav, T. N.; Yadav, R. A. Ab Initio Studies of Molecular Structures, Conformers and Vibrational Spectra of Heterocyclic Organics: I. Nicotinamide and Its N-Oxide. Spectrochim. Acta Part A Mol. Biomol. Spectrosc. 2010, 75 (1), 281–292.

(67)

Wu, Y. D.; Houk, K. N. Theoretical Study of Conformational Features of NAD+ and NADH Analogs: Protonated Nicotinamide and 1,4-Dihydronicotinamide. J. Org. Chem. 1993, 58 (8), 2043–2045.

(68)

Nakabayashi, T.; Islam, M. S.; Li, L.; Yasuda, M.; Ohta, N. Studies on External Electric Field Effects on Absorption and Fluorescence Spectra of NADH. Chem. Phys. Lett. 2014, 595, 25– 30.

(69)

Nelson, P.; Radosavljević, M.; Bromberg, S. Biological Physics: Energy, Information, Life; W.H. Freeman and Company, 2007.

(70)

Wu, Y. D.; Houk, K. N. Theoretical Evaluation of Conformational Preferences of NAD+ and NADH: An Approach to Understanding the Stereospecificity of NAD+/NADH-Dependent Dehydrogenases. J. Am. Chem. Soc. 1991, 113 (7), 2353–2358.

(71)

Drobizhev, M.; Makarov, N. S.; Tillo, S. E.; Hughes, T. E.; Rebane, A. Two-Photon Absorption Properties of Fluorescent Proteins. Nat Meth 2011, 8 (5), 393–399.

(72)

Drobizhev, M.; Tillo, S.; Makarov, N. S.; Hughes, T. E.; Rebane, A. Absolute Two-Photon Absorption Spectra and Two-Photon Brightness of Orange and Red Fluorescent Proteins. J. Phys. Chem. B 2009, 113 (4), 855–859.



(73)

Page 44 of 51

Masters, T. A.; Marsh, R. J.; Armoogum, D. A.; Nicolaou, N.; Larijani, B. B.; Bain, A. J. Restricted State Selection in Fluorescent Protein Forster Resonance Energy Transfer. J. Am. Chem. Soc. 2013, 135 (21), 7883–7890.


Page 45 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TOC Graphic



Fluorescence in NADH and NADPH is localized to the nicotinamide moiety (a), where the amide group can adopt a cis (shown) or trans form by rotating 180° around the bond linking it to the pyridine ring. NADPH differs in structure from NADH by the presence of a phosphate group (b) at the adenine (c) end of the molecule.

ACS Paragon Plus Environment

Page 46 of 51

Page 47 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Two-photon action cross section spectra and absorption polarisation ratios of (a) NADH and (b) NADPH in aqueous HEPES buffer. No differences in the 2PA absorption characteristics of NADH and NADPH were evident, including in their relative susceptibility to circularly and linearly polarised excitation which remained invariant to excitation wavelength across the two-photon resonance, averaging 0.776(±0.002). The twophoton action cross sections peak at 690 nm at a value of 0.15 GM. This occurs at a similar energy to the 1PA spectrum (c&d). 139x102mm (300 x 300 DPI)



Representative fluorescence intensity decays of 1mM NADH in aqueous solution excited at 705nm using (a) linearly polarised 2PA, (b) circularly polarised 2PA and (c) 1PA at 360 nm excitation. Weighted residuals (W.R.) are the ratio of the difference between the model and the data and the expected standard deviation, calculated using Equation 32. 62x186mm (300 x 300 DPI)


Page 48 of 51

Page 49 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Relative fluorescence intensity of the two NAD(P)H species as a function of excitation wavelength, with the short lifetime linearly polarised peak of each molecule arbitrarily scaled to 1. While the short lifetime species favours linearly polarised excitation in both NADH and NADPH (a&b), the longer lifetime species exhibits similar fluorescence intensities with both excitation polarisations (c&d). Shaded areas represent uncertainty bounds.



Representative fluorescence anisotropy decays of 1mM NADH in aqueous solution excited at 705nm using (a) linearly polarised 2PA, (b) circularly polarised 2PA and (c) 1PA at 360 nm excitation. Weighted residuals (W.R.) are the ratio of the difference between the model and the data and the expected standard deviation, calculated using Equation 35. 62x184mm (300 x 300 DPI)


Page 50 of 51

Page 51 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2PA tensor polar plots for the combined NADH and NADPH data displayed in Table 3. The distance of the line to the origin dictates the transition amplitude at each angle. Red and blue lines indicate positive and negative amplitudes, respectively. Shaded areas represent uncertainty bounds. While the short lifetime tensor is dominated by a single element (a), the long lifetime species exhibits negative lobes which rotate the direction of maximum absorption by around 3° from the single-photon S0-S1 transition (b). These features could not be resolved if the excited state population was treated as homogeneous (c). 98x261mm (300 x 300 DPI)


1 Polarised Two-Photon Absorption and Heterogeneous Fluorescence

Recommend Documents